In this article we consider the initial value problem for the -equivariant Chern–Simons–Schrödinger model in two spatial dimensions with coupling parameter . This is a covariant NLS type problem that is -critical. We prove that at the critical regularity, for any equivariance index , the initial value problem in the defocusing case () is globally wellposed and the solution scatters. The problem is focusing when , and in this case we prove that for equivariance indices , , there exist constants such that, at the critical regularity, the initial value problem is globally wellposed and the solution scatters when the initial data is -equivariant and satisfies . We also show that is equal to the minimum norm of a nontrivial -equivariant standing wave solution. In the self-dual case, we have the exact numerical values .
Cite this article
Baoping Liu, Paul Smith, Global wellposedness of the equivariant Chern–Simons–Schrödinger equation. Rev. Mat. Iberoam. 32 (2016), no. 3, pp. 751–794DOI 10.4171/RMI/898